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Relativistic length, 2 viewpoints

  1. Sep 16, 2008 #1
    Problem statement:

    Two identical cyclists ride past each other with constant velocities Va and Vb, which are close to the speed of light. Can it be that cyclist A perceives cyclist B as shorter or longer that cyclist B percieves cyclist A ? Or simply La is NOT equal to Lb ? (La-length of cyclist A as seen by cyclist B, Lb -length of cyclist B as seen by cyclist A).

    Relevant formulas:

    Relative speed V = Va+Vb/(1+(Va*Vb/c^2))
    Relative length l = lo * square root from 1-(V/c)^2


    The V from the second equasion is equal for both cyclists, since addition and multiplication are alternate. lo is also equal. So there is no difference in the way cyclists A and B see each other.

    Is this conclusion right?
    Last edited: Sep 16, 2008
  2. jcsd
  3. Sep 16, 2008 #2
    its correct if the cyclists are the same length to begin with.

    dont forget that there is also a loss of simultaneity. once you factor that in it stops seeming so impossible.
    Last edited: Sep 16, 2008
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